My Samsung Galaxy Tab felt on the street and the glass on the touch screen is broken. The display still works fine, but it is "danger to touch it", especially for kids.

When I visited repair shop, they asked for the price almost equal to the price of new device.

As it seems to work still fine, my hypothesis is that only the glass is broken, and actually display (electronic device) behind it is ok. And if I would be able to remove the broken glass and get new one (from some ordinary "window maker") and glue it on the display, everything should be ok.

Well, maybe it is not Android issue per se, but "Android Enthusiasts" are the most likely people to give reasonable answer (and indeed answers below are correct ones). The best fit of the question topic and audience, who might know the answer, is something evolving and not necessarily following the definition of "right question". What should we do with these questions, which are not right, but otherwise they are perfect fit for audience?
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Tom BurgerJul 2 '12 at 11:35

You can pick up a replacementon eBay for ~$80. It looks like they all come with the glass + the digitizer, from what I have read, they are a "combo" item. Then you can find tutorials on how to replace the screen.

If the digitizer still works and the only issue is the sharp edges, I know a bunch of folks that have (device agnostic) cracked screens with a screen protector serving as more of a finger protector on them.